Get a new hobby, this one is scary

Having recently taken up knitting, I've learned a few things concerning my erstwhile hobby.  It's twisting my brain into contorted positions a yogi could never achieve, even over the course of several lifetimes.

For me knitting is not just a hobby, but a meditative technique that frees my mind to think about well, whatever crosses it.  Most people react to my flights of mental fancy with a polite "get another hobby." That's the only polite thing they can say about how my brain works.

Those two seemingly innocuous stitches, knit and purl, once mastered exert a pull on the psyche only matched in nature by a black hole. The comparison is apt: Knitting is the black hole, and mastery of of those two stitches the event horizon. Once you cross there is no escape. Nevertheless, once inside, you discover a multiplicity of new universes. 

My previous universe was knitting a baby sweater. A kind and comfortable place. My current universe is sock knitting. In practice a sock is just a bent tube that is closed on one end. In my mind it became anything but.

In knitting, I embraced elementary school math by adjusting my gauge because I can't match the gauge of a pattern to save my life. For the average knitter gauge adjustment can feel as intimidating as making the leap from counting to calculus.  At times, just the thought of it is enough to make your eyes roll back into your head and induce a seizure. 

4th grade math was never as important as it is when you realize the gauge swatch you just knit for your sock means said sock would fit a full grown yeti. It only takes ignoring gauge once and knitting one yeti-sized sock before cracking open your child's math text to relearn calculating ratios so that the suckers will fit a real person. Once applied and happily knitting away, that gauge conversion ratio frees my mind for thought exploration.  Be afraid, be very afraid.

In this way the sock universe becomes Borg. You will be assimilated. Resistance is futile.

At a minimum, a knitted sock could probably best be described mathematically as a non linear function that would turn most mathematician's bowels to water. It sure does that to mine. Remember, I just re-embraced  4th grade math?  The series of twists traversed by a single strand of sock yarn worked toe up are mathematically more impressive than the age of the universe. And my mind begins to wander...

The function gently spirals up in size in size from a line of stitches into a cylindrical ovoid encompassing the instep. To become the heel, the function traverses a plane of stitched short rows worked back and forth. It them continues back into cylindrical form, and is ribbed before the function reaches its endpoint.  I wonder what that equation looks like??? Really? Really. Resistance is futile.

As I work steadily away on my sock, observing my work in progress brings me to the brink of mathematics, with the question "why does my sock look like THIS?" The easy answer is that it isn't finished yet. However, knitting a sock from the toe up generates shapes reminiscent of the most incomprehensible of topological transformations.  What n-fold torus can this sock form, hmmm? 

How does a mathematician really see a donut in a coffee cup? The same way I see a finished sock in a ball of yarn, that's how. I don't think Riemann had socks in mind as he worked, but that something as simple as knitting a sock can bring topological transformations to mind says a great deal about the power of both math and knitting. 

Maybe mathematicians could answer the big questions about the universe investigating socks... 

And all of this came from calculating a gauge conversion. No wonder it scares knitters.

 I'm often told "get another hobby." Now you can see why. Resistance is futile.